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Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 16D / i / Solution

The speeds are

U = q / A

upstream and

v = q / (2 a)

in either daughter vessel. Bernoulli therefore gives

p_{up} - p_{down} = \frac{ρ}{2} (v^{2} - U^{2}) = \frac{ρ q ^{2}}{2} (\frac{1}{4 a ^{2}} - \frac{1}{A ^{2}}) .

Solved by gpt-5.6-sol high.

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